This is the time of year when the must-have accessory for TV comedians seems to be a celebrity memoir: autumn 2013 autobiographers include Sir David Jason, Jennifer Saunders, Peter Kay and Jack Whitehall. But the other most desired CV entry for comics is to have written your own sitcom, and the above list demonstrates the transition in this area.

Jason is representative of a generation that tended to be involved in comedy as an actor in scripts written by other hands: Open All Hours was scripted by Roy Clarke and Only Fools and Horses by John Sullivan. Although Jason's mentor, Ronnie Barker, wrote one sitcom for himself – Clarence (1988), under the pseudonym Bob Ferris – Barker also most often served the work of other writers, although he would add some of his own lines to Dick Clement and Ian La Frenais's Porridge. Jennifer Saunders was part of the trend towards self-authored shows when she created Absolutely Fabulous for herself, while Peter Kay worked with a writing team on Phoenix Nights, which has been a common tactic for comedians, also used by Steve Coogan on the Alan Partridge shows.

Intriguingly, Davies, like Whitehall, casts himself as a teacher, continuing the odd proliferation of classroom comedies in the current schedules, following Bad Education and David Walliams' and the Dawson Brothers' Big School. Admittedly, the comedian's own pedagogic past has been a key feature of his standup material, a connection he underlines by giving his sitcom character the name "Mr Davies", although the character, first-name Dan, is a primary teacher rather than the secondary type that the performer was himself (and played in The Inbetweeners).

What happens to Mr Davies is also recognisably an extension of the comedian's solo stage shows, with sight gags involving his vast height – the teacher drives a car far too small for his legs – and plotlines turning on his incompetence with such adult requirements as mortgages and relationships.

There's also an autobiographical element in Toast of London, in that Matt Berry has created for himself the role of a deep-voiced actor, although, in the fictional version, a bad one. Again, there's a thematic overlap with another current show – Vicious, with Sir Ian McKellen and Sir Derek Jacobi – although Berry's protagonist, desperate thesp Steven Toast, is at least theoretically heterosexual, beginning and ending the opening episode in the bedrooms of would-be conquests.

Berry also seems, understandably, to have been influenced by Linehan, who wrote so well for him, and especially the surreal and fantastical streak of series such as The IT Crowd. The first Toast of London features a startling visual gag, involving an African woman who, after a mix-up at a cosmetic surgery clinic, has been given the features of one of the co-hosts of Strictly Come Dancing, and not, as might have been slightly more plausible, Tess Daly.

There's an understandable tendency for a self-written sitcom to be essentially a character sketch, a monologue with occasional interruptions, and Davies and Berry feature in almost every scene of their opening episodes. The test of the shows will be whether – as was managed by Saunders in Absolutely Fabulous and Tina Fey in 30 Rock – the writers can show increasing interest in the supporting cast.

The trend towards actor-writers in sitcoms has probably been encouraged by the example of Ricky Gervais and Stephen Merchant, who not only scripted and delivered The Office and Extras but also directed them as well, which gives Whitehall, Davies and Berry something else to aim for.

Both Man Down and Toast of London are promising examples of their different sitcom traditions – slapstick-silly and darkish-surreal respectively – but commissioners should bear in mind that Ronnie Barker's least successful comedy was the one he wrote himself: the majority of the most memorable comedies have had a division of labour between typing and speaking.